Mode compute = 6 Monte Carlo routine

[qazi.haque]

Hi Johannes,

I have been trying to estimate a small scale NK model with deep habits using my own MATLAB codes. However, it seems to be that csminwel fails to find the correct mode. That's why I am now trying to use Monte Carlo routine as in mode_compute = 6 to get the mean and covariance matrix for the jumping distribution in the MH algorithm. Toward that purpose I have tried to write up a MATLAB code for that in spirit of what mode_compute = 6 is doing. But for some reason it's not working. Could you please provide me with the mode_compute = 6 code that DYNARE is using so that I can have a look at it for better understanding?

Moreover, could you briefly explain what's the reasoning behind the updating scheme for mean and covariance matrix which DYNARE is using in mode_compute = 6 as stated here:

http://www.dynare.org/DynareWiki/MonteCarloOptimization

Please find attached the MATLAB code I have written in spirit to mode_compute = 6 as described in the above link.

Looking forward to your response.

Cheers,
Qazi

[jpfeifer]

mode_compute=6 is basically a simulated annealing type routine. Instead of programming something like this yourself, I would recommend using any global optimizer freely available. Note also that any jumping covariance matrix works. You could just pick a scaled identity matrix to start your MCMC and once it has converged to a region of higher likelihood, start again with mode-finding. This is essentially what mode_compute=6 does.

[qazi.haque]

If I understand this correctly, for the MH algorithm, we don't need to start exactly at the mode but from a point with a high posterior density value and to use a good covariance matrix for the jumping distribution. Now what if I initially run a MH algorithm with the mean of the jumping distribution set to the prior mean and the variance-covariance matrix to scaled identity matrix. I then run this MH algorithm, say for 1000000 draws and compute the mean values of the last 500,000 draws (conditional on convergence). Next, I run my 'proper' MH algorithm, now with the starting value set to the mean I have just calculated from the previous step and the variance-covariance of the jumping distribution set to the inverse of the hessian computed at the calculated mean.

What's your view about such a procedure? I am trying to do it this way because often times, as you know, Newton type algorithm like Chris Sim's 'csminwel' gets stuck due to cliffs in the log posterior.

Thanks again.

[jpfeifer]

This is perfectly fine. You just have to treat the initial draws as a burnin. Theory tells you that, as long as the regularity conditions are met, any jumping covariance should work (but potentially only in close to infinite time/infinitely many draws). I would recommend using e.g. CMAES for mode finding first. It is freely available.

[qazi.haque]

Thanks for your suggestion. Just to clarify one more thing - is it the case that 'repeated' application of CMAES is essentially similar to mode_compute 6 in dynare?

[jpfeifer]

No, repeated application of a MCMC would correspond to mode_compute=6. CMAES is simply a global optimizer like simulated annealing. It tends to work pretty well.